(specific problems with MediaWiki and motivation for replacing it; also things I like about it and wish to copy/retain)
For example, I want a "What I like about ..." and "What I don't like about ..." section. I want them both to be on the same page (at least until they grow to be really big, at which point I might want to separate them), but I want them to be separate entities, which I can include separately in other paces, which have their own revision histories, etc.
You have to click Edit, wait for the page to load, scroll to the bottom, type in the full link to the category name (and spell it right!)...
An example of such a one can be found on Wikipedia: http://en.wikipedia.org/w/index.php?title=Template:Todo&action=edit . They even have a category devoted simply to keeping track of all their ugly ("esoteric") templates.
I would want to use a Ruby-base templating language for templates so that even complex logic could be expressed beautifully and succinctly.
So if I have a stale copy of a page and sections have been added since loading the page, the edit links will lead to the wrong section!
Click "Add to category". A list of commonly used / last used categories shows up immediately (Ajax). You click on one and it adds it (in the background, with Ajax).
If your desired category isn't in the list, just start typing it in the search box. It will start listing matches as you type. Either finish typing or select a match from the list.
*(unless this option was disabled for current user)
I often take an index/category page, middle click on each link to open in a new tab, and then I have to click edit on every single one of those pages to start edit mode. I want to get to edit mode sooner, easier!!
(Including for search results... show edit link for every page listed as a hit)
Rather than just show the matching sentence as context for keyword searches, show the whole section? And have edit link to edit that section?
Perhaps I would do away with the idea of a stand-alone article and require every article to be associated with at least one category.
(That is, the categories themselves would be the only pages. Articles could not be pages -- they could only be included on article pages.)
Then to view articles, you search for / go to the category's page, which:
Another way of looking at it is: Articles themselves would not have titles; instead, they would belong to categories with the name of the title you want to give the article. So you see that the category itself is the page, which then just includes all of its member articles onto the page.